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具有Bernoulli休假的不可见M/M/1重试排队模型的进队策略分析

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具有Bernoulli休假的不可见M/M/1重试排队模型的进队策略分析 高珊1, 王金亭2, Tien Van Do31. 阜阳师范学院数学与统计学院, 阜阳 236037;
2. 北京交通大学理学院, 北京 100044;
3. Analysis, Design and Development of ICT systems(AddICT) Laboratory, Budapest University of Technology and Economics, Budapest, Hungary Analysis of the Entrance Strategies for an Unobservable M/M/1 Retrial Queue with Bernoulli Vacation GAO Shan1, WANG Jinting2, DO Tien Van31. Department of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China;
2. Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China;
3. Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, Hungary
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摘要考虑具有常重试率和Bernoulli休假的M/M/1重试排队,到达系统的顾客仅知道服务台的状态.如果在顾客到达时刻服务台正忙,则顾客或以概率q加入到重试组中,或以概率1-q止步.在每次服务结束后,服务台或者以概率p开始一次休假,或者以概率1-p保持空闲状态.基于收入-支出结构,得到了个体最优进队策略,社会净收益最优进队策略和利润最优进队策略.对于这些最优进队概率的大小顺序我们给出了详细的证明.最后,给出了数值例子来阐述进队策略的影响.
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收稿日期: 2015-12-06
PACS:O226
基金资助:国家自然科学基金(No.61672006,71571014,71390334,11301306)以及安徽省高等学校省级自然科学研究(No.KJ2014ZD21,KJ2015A182,KJ2015A191,KJ2016A875)资助项目.
引用本文:
高珊, 王金亭, Tien Van Do. 具有Bernoulli休假的不可见M/M/1重试排队模型的进队策略分析[J]. 应用数学学报, 2017, 40(1): 106-120. GAO Shan, WANG Jinting, DO Tien Van. Analysis of the Entrance Strategies for an Unobservable M/M/1 Retrial Queue with Bernoulli Vacation. Acta Mathematicae Applicatae Sinica, 2017, 40(1): 106-120.
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